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Multiple same-size linear solver

25 May 2009 (Updated 26 May 2010)

Solve multiple systems of linear equations of the same size

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Description

Sometime we need to solve a bunch of small linear (least-square) systems of the same size. This function can accomplish this task conveniently.

The system matrix and RHS are passed as 3D arrays.

Furthermore, calling syntax can support two simplifications:
- same RHS for all systems; or
- single RHS for each system.

Followed an idea from Tim Davis (using sparse)

Acknowledgements

This submission has inspired the following:
Inversion every 2D slice for arbitrary Multi-dimension array. , Free-knot spline approximation

MATLAB release

MATLAB 7.8 (R2009a)

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Everyone's Tags	least square, linear equations, linear system
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Comments and Ratings (1)
27 Apr 2011	Cole Van Vlack	Hi Bruno, I tried your function on a large array (eg. 551000000), it occupies too much memory. It will take at least 5 times memory as the initial data package. And most of the memory cost is to store the sparse indexes. Is there any way to reduce the memory consuming? Thanks! Cheers, Xiaodong

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Updates
27 May 2009	Minor typo correction
11 Aug 2009	- A wrapper to call with arrays that loop on the third dimension - Multi matrix-products
26 May 2010	Correct miss-leading MultiProd H1 line